Find the polar co-ordinates of points whose Cartesian co-ordinates are

1.	Find the polar co-ordinates of points whose Cartesian co-ordinates are: (1,√3 )
Answer» (x, y) = ( 1,√3) ∴ r =\(\sqrt{x^2+y^2} = \sqrt{1+3} = \sqrt4 = 2\) tan θ = \(\frac{y}{x} = \frac {\sqrt3}{1} =\sqrt3\) Since the given point lies in the 1st quadrant, θ = 60° …[∵ tan 60° = √3] ∴ the required polar co-ordinates are (2, 60°).

Find the polar co-ordinates of points whose Cartesian co-ordinates are: (1,√3 )

Answer»

(x, y) = ( 1,√3)

∴ r =\(\sqrt{x^2+y^2} = \sqrt{1+3} = \sqrt4 = 2\)

tan θ = \(\frac{y}{x} = \frac {\sqrt3}{1} =\sqrt3\)

Since the given point lies in the 1st quadrant,

θ = 60° …[∵ tan 60° = √3]

∴ the required polar co-ordinates are (2, 60°).